Binary period distributions

The orbital period distribution $f(P)$ is one of the binary-population ingredients used alongside the mass-ratio and eccentricity distributions. progenax currently exposes three direct period samplers and one mass-dependent routing helper.

There is no public Moe17Period class in this checkout. The full Moe & Di Stefano mass-ratio and multiplicity machinery lives in progenax.imf.binary, especially MoeDiStefano2017 and BinaryIMF.

Log-uniform¶

LogUniformPeriod samples uniformly in $\log_{10} P$:

from progenax.binaries import LogUniformPeriod

period_dist = LogUniformPeriod(log_P_min=0.0, log_P_max=8.0)
periods_days = period_dist.sample(key, 10000)

The returned values are periods in days, not $\log P$.

Log-normal¶

LogNormalPeriod samples a normal distribution in $\log_{10} P$ and returns periods in days:

from progenax.binaries import LogNormalPeriod

solar = LogNormalPeriod(mu_log_P=4.8, sigma_log_P=2.3)
periods_days = solar.sample(key, 10000)

The defaults follow the broad solar-type binary period distribution.

Sana OB periods¶

SanaOBPeriod samples the short-period-biased massive-star distribution from Sana et al. (2012):

from progenax.binaries import SanaOBPeriod

ob = SanaOBPeriod(log_P_min=0.3, log_P_max=3.5, power=-0.55)
periods_days = ob.sample(key, 10000)

This distribution is appropriate for O/B-type primaries, not for a generic low-mass field population.

Mass-dependent routing¶

For a mixed population, use sample_mass_dependent_orbits to route low- and high-mass primaries to different period and eccentricity models:

from progenax.binaries import (
    LogNormalPeriod,
    MassDependentBinaryConfig,
    MoeEccentricity,
    SanaOBPeriod,
    ThermalEccentricity,
    sample_mass_dependent_orbits,
)

config = MassDependentBinaryConfig(
    m_break=8.0,
    low_mass_period=LogNormalPeriod(),
    high_mass_period=SanaOBPeriod(),
    low_mass_eccentricity=ThermalEccentricity(),
    high_mass_eccentricity=MoeEccentricity(),
)

periods_days, eccentricities = sample_mass_dependent_orbits(
    primary_masses, config, key
)

Period-mass-ratio coupling¶

The Moe & Di Stefano (2017) joint distribution is non-separable: mass-ratio statistics depend on primary mass and period, and eccentricity depends on period. progenax currently exposes these pieces separately rather than as one public all-parameters sampler.

from progenax.imf import BinaryIMF, MoeDiStefano2017, PowerLawIMF

binary_imf = BinaryIMF(
    primary_imf=PowerLawIMF.kroupa(),
    q_distribution=MoeDiStefano2017(),
)
m1, m2, is_binary = binary_imf.sample_systems(key, 1000)

Domain of validity¶

1. Period range. The implemented samplers encode finite period ranges or broad log-normal support; compact binaries and extremely wide marginally bound systems require extra physics.

2. Population dependence. LogNormalPeriod and SanaOBPeriod are calibrated for different primary-mass regimes. Use the routing helper for mixed populations.

3. IC-time only. Dynamical encounters and stellar evolution can alter periods after birth; those belong in downstream evolution.

Implementation, validation & references¶

• In code: src/progenax/binaries/period.py (LogUniformPeriod, LogNormalPeriod, SanaOBPeriod) and src/progenax/binaries/mass_dependent.py (MassDependentBinaryConfig, sample_mass_dependent_orbits); the full Moe & Di Stefano machinery lives in src/progenax/imf/binary/. See the binaries API.

• Validated in: binary-aware recovery.

• Primary sources: Sana et al. (2012) provides the OB-period anchor; the broader mass-dependent binary-statistics reference is Moe & Di Stefano (2017). Full notes in the bibliography; see also Multiplicity statistics (Moe & Di Stefano 2017) and Mass-ratio distributions.